Common Core State Standards for Mathematics
Grade 7
Geometry
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
7.G.B.4
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
7.G.B.6
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Grade 8
Functions
Define, evaluate, and compare functions.
Use functions to model relationships between quantities.
8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Geometry
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
8.G.C.9
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Ohio Mathematics Academic Content Standards (2001)
Measurement Standard
Benchmarks (8–10)
B.
Use formulas to find surface area and volume for specified three-dimensional objects accurate to a specified level of precision.
E.
Estimate and compute various attributes, including length, angle measure, area, surface area and volume, to a specified level of precision.
Grade Level Indicators (Grade 8)
3.
Use appropriate levels of precision when calculating with measurements.
10.
Use conventional formulas to find the surface area and volume of prisms, pyramids and cylinders and the volume of spheres and cones to a specified level of precision.
Patterns, Functions and Algebra Standard
Benchmarks (8–10)
D.
Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.
Grade Level Indicators (Grade 8)
8.
Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems.
Grade Level Indicators (Grade 10)
3.
Solve equations and formulas for a specified variable; e.g., express the base of a triangle in terms of the area and height.
10.
Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.
Principles and Standards for School Mathematics
Measurement Standard
Apply appropriate techniques, tools, and formulas to determine measurements.
Expectations (6–8)
select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision;
Expectations (9–12)
understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders;